The structures of three Na–Pb compounds, γ, δ and δ′, have remained incompletely solved for nearly 60 years. The space group, lattice parameters and positions of the Pb atoms of these three structures have been determined, but the positions of the Na atoms are still unknown. In this work, the First-Principles Assisted Structure Solution (FPASS) method [Meredig & Wolverton (2013). Nat. Mater. 12, 123–127] has been used to complete the description of these three structures using only experimental information available from the literature as input. The paper also discusses the relative advantages of constrained crystal structure prediction tools, like FPASS, in comparison to conventional crystal structure prediction methods in reference to their abilities to complete the solution of other unsolved structures.
Supporting information
Crystal data top
Na9Pb4 | V = ? Å3 |
Mr = ? | Z = 2 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.4700 Å | × × mm |
c = 30.4100 Å | |
Crystal data top
Na9Pb4 | V = ? Å3 |
Mr = ? | Z = 2 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.4700 Å | × × mm |
c = 30.4100 Å | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | |
Pb1 | 0.0000 | 0.0000 | 0.0500 | | |
Pb2 | 0.3333 | 0.6667 | 0.3000 | | |
Na1 | 0.3333 | 0.6667 | 0.7500 | | |
Na2 | 0.3333 | 0.6667 | 0.6357 | | |
Na3 | 0.0000 | 0.0000 | 0.3166 | | |
Na4 | 0.3333 | 0.6667 | 0.4087 | | |
Na5 | 0.3333 | 0.6667 | 0.5198 | | |
Crystal data top
Na5Pb2 | V = ? Å3 |
Mr = ? | Z = 3 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.5400 Å | × × mm |
c = 23.1500 Å | |
Crystal data top
Na5Pb2 | V = ? Å3 |
Mr = ? | Z = 3 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.5400 Å | × × mm |
c = 23.1500 Å | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | |
Pb1 | 0.0000 | 0.0000 | 0.0700 | | |
Na1 | 0.3333 | 0.6667 | 0.3097 | | |
Na2 | 0.0000 | 0.0000 | 0.2150 | | |
Na3 | 0.0000 | 0.0000 | 0.5000 | | |
Crystal data top
Na13Pb5 | V = ? Å3 |
Mr = ? | Z = 2 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.5100 Å | × × mm |
c = 40.3900 Å | |
Crystal data top
Na13Pb5 | V = ? Å3 |
Mr = ? | Z = 2 |
Hexagonal, ? | ? radiation, λ = ? Å |
a = 5.5100 Å | × × mm |
c = 40.3900 Å | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | |
Pb1 | 0.0000 | 0.0000 | 0.2500 | | |
Pb2 | 0.3333 | 0.6667 | 0.4500 | | |
Pb3 | 0.3333 | 0.6667 | 0.3700 | | |
Na1 | 0.0000 | 0.0000 | 0.0000 | | |
Na2 | 0.3333 | 0.6667 | 0.2883 | | |
Na3 | 0.0000 | 0.0000 | 0.4167 | | |
Na4 | 0.3333 | 0.6667 | 0.8826 | | |
Na5 | 0.0000 | 0.0000 | 0.1666 | | |
Na6 | 0.3333 | 0.6667 | 0.7897 | | |
Na7 | 0.3333 | 0.6667 | 0.5316 | | |
Experimental details
| (delta-prime) | (delta) | (gamma) |
Crystal data |
Chemical formula | Na9Pb4 | Na5Pb2 | Na13Pb5 |
Mr | ? | ? | ? |
Crystal system, space group | Hexagonal, ? | Hexagonal, ? | Hexagonal, ? |
Temperature (K) | ? | ? | ? |
a, c (Å) | 5.4700, 30.4100 | 5.5400, 23.1500 | 5.5100, 40.3900 |
V (Å3) | ? | ? | ? |
Z | 2 | 3 | 2 |
Radiation type | ?, λ = ? Å | ?, λ = ? Å | ?, λ = ? Å |
µ (mm−1) | ? | ? | ? |
Crystal size (mm) | × × | × × | × × |
|
Data collection |
Diffractometer | ? | ? | ? |
Absorption correction | ? | ? | ? |
No. of measured, independent and observed (?) reflections | ?, ?, ? | ?, ?, ? | ?, ?, ? |
Rint | ? | ? | ? |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | ?, ?, ? | ?, ?, ? | ?, ?, ? |
No. of reflections | ? | ? | ? |
No. of parameters | ? | ? | ? |
No. of restraints | ? | ? | ? |
Δρmax, Δρmin (e Å−3) | ?, ? | ?, ? | ?, ? |